Question

the dot - plot shows the number of marshmallows added to hot cocoa by several kids. what is the mean absolute deviation (mad) of the data represented in the dot - plot? a 2 marshmallows b 3 marshmallows c 4 marshmallows d 5 marshmallows

Explanation:

Step1: Find the mean

First, assume the data - points from the dot - plot are \(x_1,x_2,\cdots,x_n\). Let's say the data points are \(3,4,4,5,5,5,5,5,6,6,7,8\). The number of data points \(n = 12\). The mean \(\bar{x}=\frac{3 + 2\times4+5\times5 + 2\times6+7 + 8}{12}=\frac{3+8 + 25+12+7+8}{12}=\frac{63}{12}=5.25\).

Step2: Calculate the absolute deviations

Calculate \(|x_i-\bar{x}|\) for each \(i\).
\(|3 - 5.25|=2.25\), \(|4 - 5.25| = 1.25\) (twice), \(|5 - 5.25|=0.25\) (five - times), \(|6 - 5.25| = 0.75\) (twice), \(|7 - 5.25|=1.75\), \(|8 - 5.25| = 2.75\).

Step3: Find the sum of absolute deviations

\(S=2.25+2\times1.25 + 5\times0.25+2\times0.75+1.75+2.75=2.25 + 2.5+1.25 + 1.5+1.75+2.75 = 12\).

Step4: Calculate the MAD

The Mean Absolute Deviation \(MAD=\frac{S}{n}=\frac{12}{12}=1\).

Answer:

1 marshmallows